The Everton midfielder has been listed among those linked with taking up an assisting role for the newly appointed Three Lions boss ahead of this summer's Euro 2012 campaign
The two join Hodgson's former Fulham colleague, Ray Lewington, on the list of possible candidates for a coaching role during this summer's tournament.
Speculation surrounding the Evertonian's involvement was sparked after a Twitter conversation between himself and his brother Gary Neville, where he responded to a comment about being linked with the job by saying: "No comment, you will tell sky!"
He also asked his brother: "What kind of coach do u [sic] think I'd be Gary? Would u of liked me as ur [sic] coach?"
It is thought that Hodgson has been given a full licence by the Football Association to ring the changes, and that the 64-year-old is looking for a young, emerging coach to fill the assistant role.
And with Neville currently completing his coaching badges at Everton and Shearer having being an influential figure on the international scene as well as having management experience, they could fit the mould.
The Toffees' skipper has also picked up international coaching experience recently, assisting the England Under-21s preparation for their clash with Belgium in February, while regular coach Stuart Pearce took temporary charge of the senior side.